This invention relates generally to fiber optic gyroscopes of the kind discussed at length in U.S. Pat. No. 5,278,631, issued Jan. 11, 1994, to Hollinger et al., for a Closed Loop Fiber Optic Gyroscope with Signal Processing Arrangement for Improved Performance; U.S. Pat. No. 5,280,339 issued Jan. 18, 1994, to Hollinger et al., for a Closed Loop Fiber Optic Gyroscope with Fine Angle Resolution; U.S. Pat. No. 5,309,220, issued May 3, 1994, to Hollinger et al., for a Closed Loop Fiber Optic Gyroscope with Reduced Sensitivity to Electronic Drift; and U.S. Pat. No. 5,504,580 issued Apr. 2, 1996, to Hollinger et al., for a Tuned Integrated Optic Modulator on a Fiber Optic Gyroscope; all of which are incorporated herein by reference. More particularly, it relates to a scheme for increasing the sensitivity of an interferometric fiber optic gyroscope.
The sensitivity of an interferometric fiber optic gyroscope can be expressed as a function of the random walk coefficient of noise. A significant component of the random walk coefficient is the relative intensity noise (RIN). Noise in general can be described as the mean square fluctuations &lt;.DELTA.n.sup.2 &gt; in the number of photoelectrons n emitted from a photodetector illuminated over an area A during an observation time .tau.. In the case of emission caused by polarized broadband light incident upon the photodetector, EQU &lt;.DELTA.n.sup.2 &gt;=&lt;n&gt;+&lt;n&gt;.sup.2 ( 1)
This equation holds true where the illumination area A is less than the coherence area A.sub.c of the source and the observation time .tau. is less than the coherence time .tau..sub.c of the source. For A=A.sub.c and .tau.=.tau..sub.c, Equation 1 yields the fluctuations within one phase space cell whose volume in configuration space is A.sub.c c.tau..sub.c, where c is the speed of light.
The first term, &lt;n&gt;, in the righthand side of Eq. 1, is the shot-noise and the second term, &lt;n&gt;.sup.2, is the excess photon noise due to the beating of various Fourier components within the broadband spectrum of the light source. Since the light source power at the photodetector is normally greater than 1.0 .mu.w, the largest contributor to RIN will be the excess noise term, &lt;n&gt;.sup.2.
If the broadband radiation is unpolarized and is observed over a detector area A during the time .tau., it will occupy a volume of Ac.tau.. It follows then that there will be m phase space cells contained in this volume, such that EQU m=pA.tau./(A.sub.c .tau..sub.c) (2)
where p is the number of polarization states PA1 where A.sub.c /A.apprxeq.1 for a Gaussian beam.
(p=2 for unpolarized light; p=1 for polarized light).
Variable p in Equation 2 takes into account the lack of correlation between photons with different polarization states. Typically, m is much greater than one, since .tau. is much greater than .tau..sub.c and A is greater than A.sub.c. Since the fluctuations in noise among the m phase space cells are uncorrelated and &lt;n&gt;/m electrons are emitted from each cell, the total mean square fluctuations are defined by EQU &lt;.DELTA.n.sup.2 &gt;=m&lt;n&gt;/m+(&lt;n&gt;/m).sup.2 ! (3)
and, therefore, EQU &lt;.DELTA.n.sup.2 &gt;=&lt;n&gt;+&lt;n&gt;.sup.2 /m (4)
Substituting for m using Equation 2, EQU &lt;.DELTA.n.sup.2 &gt;=&lt;n &gt;+A.sub.c .tau..sub.c &lt;n&gt;.sup.2 /(pA.tau.)(5)
Since the coherence time of the light source .tau..sub.c is inversely proportional to the optical bandwidth B.sub.1 and the observation time .tau. is inversely proportional to the detector bandwidth B.sub.2, the ratio of B.sub.1 to B.sub.2 can be substituted for the ratio of .tau. to .tau..sub.c in Equation 2: EQU m=pA.tau./(A.sub.c .tau..sub.c)=pAB.sub.1 /(A.sub.c B.sub.2)(6)
and EQU &lt;.DELTA.n.sup.2 &gt;=&lt;n&gt;+A.sub.c B.sub.2 &lt;n&gt;.sup.2 /(pAB.sub.1)(7)
Substituting the photocurrent I of the photodetector for the number n of electrons emitted, the photocurrent fluctuation is defined by EQU &lt;.DELTA.I.sup.2 &gt;=2eB.sub.2 &lt;I&gt;+2B.sub.2 &lt;I&gt;.sup.2 /(p.DELTA..upsilon.)(8)
where &lt;I&gt; is the mean detected photocurrent, e is the electron charge, .DELTA..upsilon. is the optical linewidth defined by EQU .DELTA..upsilon.=.intg.P(.upsilon.)d.upsilon.!.sup.2 /.intg.P.sup.2 (.upsilon.)d.upsilon.! (9)
and P(.upsilon.) is the power-spectral-density of the light source.
The relative intensity noise (RIN) can be expressed as the ratio of the photocurrent fluctuation to the product of the mean square of the D.C. current, &lt;I&gt;.sup.2, and the detector bandwidth B.sub.2. Thus EQU RIN=&lt;.DELTA.I.sup.2 &gt;/(&lt;I&gt;.sup.2 B.sub.2)=2/(p.DELTA..upsilon.)(10)
From Eq. 10, it can be seen that the RIN of polarized light, where p=1, is twice that of unpolarized light (p=2). Similarly, the contribution of RIN to the random walk coefficient is dependent on whether the detected light is polarized. Therefore, the random walk coefficient will be significantly reduced when the light is not polarized.
The gyroscopes previously noted above utilize linearly polarized light for sensing rotational rate and therefore exhibit the RIN characteristics attendant with a system using a single polarization. It would be desirable to reduce the random walk coefficient of noise in fiber optic gyroscopes without sacrificing their accuracy.